Validation of Subject Specific Computed Tomography-based Finite Element Models of the Human Proximal Tibia using Full-field Experimental Displacement Measurements from Digital Volume Correlation

Quantitative computed tomography-based finite element (QCT-FE) modeling is a computational tool for predicting bone’s response to applied load, and is used by musculoskeletal researchers to better understand bone mechanics and their role in joint health. Decisions made at the modeling stage, such as the method for assigning material properties, can dictate model accuracy. Predictions of surface strains/stiffness from QCT-FE models of the proximal tibia have been validated against experiment, yet it is unclear whether these models accurately predict internal bone mechanics (displacement). Digital volume correlation (DVC) can measure internal bone displacements and has been used to validate FE models of bone; though, its use has been limited to small specimens. The objectives of this study were to 1) establish a methodology for high-resolution peripheral QCT (HR-pQCT) scan acquisition and image processing resulting in low DVC displacement measurement error in long human bones, and 2) apply different density-modulus relationships and material models from the literature to QCT-FE models of the proximal tibia and identify those approaches which best predicted experimentally measured internal bone displacements and related external reaction forces, with highest explained variance and least error. Using a modified protocol for HR-pQCT, DVC displacement errors for large scan volumes were less than 19μm (0.5 voxels). Specific trabecular and cortical models from the literature were identified which resulted in the most accurate QCT-FE predictions of internal displacements (RMSE%=3.9%, R2>0.98) and reaction forces (RMSE%=12.2%, R2=0.78). This study is the first study to quantify experimental displacements inside a long human bone using DVC. It is also the first study to assess the accuracy of QCT-FE predicted internal displacements in the tibia. Our results indicate that QCT-FE models of the tibia offer reasonably accurate predictions of internal bone displacements and reaction forces for use in studying bone mechanics and joint health

Computationally-Optimized Bone Mechanical Modeling from High-Resolution Structural Images

Image-based mechanical modeling of the complex micro-structure of human bone has shown promise as a non-invasive method for characterizing bone strength and fracture risk in vivo. In particular, elastic moduli obtained from image-derived micro-finite element (μFE) simulations have been shown to correlate well with results obtained by mechanical testing of cadaveric bone. However, most existing large-scale finite-element simulation programs require significant computing resources, which hamper their use in common laboratory and clinical environments. In this work, we theoretically derive and computationally evaluate the resources needed to perform such simulations (in terms of computer memory and computation time), which are dependent on the number of finite elements in the image-derived bone model. A detailed description of our approach is provided, which is specifically optimized for μFE modeling of the complex three-dimensional architecture of trabecular bone. Our implementation includes domain decomposition for parallel computing, a novel stopping criterion, and a system for speeding up convergence by pre-iterating on coarser grids. The performance of the system is demonstrated on a dual quad-core Xeon 3.16 GHz CPUs equipped with 40 GB of RAM. Models of distal tibia derived from 3D in-vivo MR images in a patient comprising 200,000 elements required less than 30 seconds to converge (and 40 MB RAM). To illustrate the system's potential for large-scale μFE simulations, axial stiffness was estimated from high-resolution micro-CT images of a voxel array of 90 million elements comprising the human proximal femur in seven hours CPU time. In conclusion, the system described should enable image-based finite-element bone simulations in practical computation times on high-end desktop computers with applications to laboratory studies and clinical imaging

Mapping anisotropy improves QCT-based finite element estimation of hip strength in pooled stance and side-fall load configurations

Hip fractures are one of the most severe consequences of osteoporosis. Compared to the clinical standard of DXA-based aBMD at the femoral neck, QCT-based FEA delivers a better surrogate of femoral strength and gains acceptance for the calculation of hip fracture risk when a CT reconstruction is available. Isotropic, homogenised voxel-based, finite element (hvFE) models are widely used to estimate femoral strength in cross-sectional and longitudinal clinical studies. However, fabric anisotropy is a classical feature of the architecture of the proximal femur and the second determinant of the homogenised mechanical properties of trabecular bone. Due to the limited resolution, fabric anisotropy cannot be derived from clinical CT reconstructions. Alternatively, fabric anisotropy can be extracted from HR-pQCT images of cadaveric femora. In this study, fabric anisotropy from HR-pQCT images was mapped onto QCT-based hvFE models of 71 human proximal femora for which both HR-pQCT and QCT images were available. Stiffness and ultimate load computed from anisotropic hvFE models were compared with previous biomechanical tests in both stance and side-fall configurations. The influence of using the femur-specific versus a mean fabric distribution on the hvFE predictions was assessed. Femur-specific and mean fabric enhance the prediction of experimental ultimate force for the pooled, i.e. stance and side-fall, (isotropic: r2=0.81, femur-specific fabric: r2=0.88, mean fabric: r2=0.86,p<0.001) but not for the individual configurations. Fabric anisotropy significantly improves bone strength prediction for the pooled configurations, and mapped fabric provides a comparable prediction to true fabric. The mapping of fabric anisotropy is therefore expected to help generate more accurate QCT-based hvFE models of the proximal femur for personalised or multiple load configurations

Image analysis tool for the characterisation of bone turnover in the appendicular skeleton

Osteoporosis is a disease characterised by reduced bone mass and altered microarchitecture leading to an increased risk of fracture. The consequences of osteoporosis include reduced quality of life and pain, associated with fractures. Its financial burden on health services are significant. Characterisation of osteoporosis using imaging techniques is therefore important. Peripheral Quantitative Computed Tomography (pQCT) is a cross-sectional imaging method which is used to scan bones in the appendicular skeleton. pQCT imaging may be particularly useful in clinical groups where changes in bone mineral density (BMD) and structure are known to occur in the limbs. Two such groups are patients following spinal cord injury (SCI) or anterior cruciate ligament (ACL) injury. Aims. This project aimed to develop analysis techniques to characterise bone in pQCT images. Their purpose was to describe localised changes within pQCT images of the bone, as opposed to the standard global measurements. Methods. Fully automated segmentation and registration software was developed and tested followed by two independent processing algorithms. The first generates spatial maps to characterise local changes in BMD. This is achieved using both quadrant analysis software and a voxel-based approach, the latter comparing pairs of images and generating a voxel-by-voxel ΔBMD map of changes in BMD. The second processing algorithm uses morphological granulometries to investigate the bone microarchitecture. Results. Evaluation of these image analysis methods was carried out using two clinical studies. The first investigates acute longitudinal changes in the distal tibia (DT) and distal femur (DF) post-motor-complete-SCI using pQCT. Images from 15 subjects (13M, 2F) with a mean age of 36y±19y, were acquired at 4-monthly intervals during the first year post-injury. The second comprises of ACL injury subjects, with imaging of the injured and contralateral proximal tibia (PT) and distal femur before (n=19, 18M 1F, 30y±9y of age) and after (n=8, 8M 0F, 31y±9y of age) surgical ACL reconstruction. The software developed to automatically segment bone from surrounding structures was successful: 98% success rate for epiphyseal tibial regions, 67% success rate for the distal femur. Registration of images was then performed and the spatial analysis methods to automatically produce quadrants of trabecular bone were applied, displaying individual results graphically. The voxel based analysis method was developed, tested and applied to produce ΔBMD maps, utilising statistical inference and corrections for multiple comparisons using a false-discovery rate technique. These maps characterised localised changes in BMD between pairs of both longitudinal and contralateral images. Software was also developed to apply morphological granulometries to pQCT images, calculating global and local pattern spectrum moments. On application of the analysis methods to the longitudinal SCI images, the BMD and microarchitecture findings were observed to be disparate amongst subjects, with large variations in bone characteristics both globally and regionally. The quadrant and voxel based analysis methods provided information on longitudinal regional changes in each subject, indicating individual patterns of change. Structural analysis of bone microarchitecture using granulometries was demonstrated to have potential as a useful adjunct to BMD in identifying SCI subjects more susceptible to rapid bone loss. The analysis methods were also successfully applied to the ACL injury subjects. Following segmentation and registration, the total and trabecular BMD in the injured knee was observed to be significantly lower than that of the contralateral control knee pre-operatively for both the PT and DF (p<0.05). Post-operatively the total and trabecular BMD in the injured DF remained significantly low (p<0.05), however the PT demonstrated significantly lower BMD in the injured leg for the trabecular bone only (p<0.05). Reduced BMD in the PT post-operatively in humans is a novel observation, and indicates a benefit afforded by segmenting trabecular from cortical bone. Regional analysis using quadrants indicated some anatomical variation in bone loss within the injured limb, although it is acknowledged that these are preliminary findings which would require to be confirmed in larger studies. The voxel ΔBMD maps generally indicated global losses across the bones of the ACL injured leg both pre-operatively and post-operatively. No consistent patterns were obtained in the ΔBMD maps for these subjects, suggesting individual patterns of response to ACL injury. The structural information provided by granulometric analysis was limited for the ACL study. Conclusions. Automated software has been developed to characterise bone in pQCT images of the appendicular skeleton. It has been successfully applied to two clinical studies, facilitating localised changes in bone density to be demonstrated and descriptions of microarchitecture to be provided. The SCI subjects appear to have individualistic responses to injury, with a wide range of changes in bone density and microarchitecture observed. ACL injury patients all lost bone mass, but patterns of change were variable. The analysis methods developed to permit characterisation of bones in individual subjects, are proposed to be of value in both clinical and research domains exploring bone mass and microarchitecture, with the ultimate goals being the prediction of fracture risk and tailoring therapy for the individual

Contributions of anisotropic and heterogeneous tissue modulus to apparent trabecular bone mechanical properties

The highly optimized hierarchical structure of trabecular bone is a major contributor to its remarkable mechanical properties. At the micro-scale level, individual plate-like and rod-like trabeculae are interconnected, forming a complex trabecular architecture. It is widely believed that bone strength, an important mechanical characteristic that describes the capability of bone to resist fracture, is largely determined by the tissue-level material properties of these microscopic trabecular elements. However, due to the complicated microstructure and irregular morphology of trabecular bone, a link between the tissue-level and the apparent level mechanics in trabecular bone has never been established. Thus, the goal of this thesis is to examine the tissue-level material properties of trabecular bone and their contribution to apparent-level bone mechanics, and ultimately to improve our fundamental understanding and assessment of bone strength in diseased and healthy patients. At the micro-scale level, plate-like and rod-like trabeculae are distinctly aligned along different orientations on the anatomical axis of the skeleton. Also, the highly organized underlying ultrastructure of bone tissue suggests trabecular bone might possess an anisotropic tissue modulus, i.e. different modulus in the axial and lateral cross-section of a trabecula. In this thesis, we studied this tissue-level anisotropy by examining mechanical properties of individual trabecular plates and rods aligned longitudinally, obliquely, and transversely on the anatomical axis using micro-indentation. We discovered that, despite the different orientations of trabeculae, tissue moduli are higher in the axial direction than in the lateral direction for both plates and rods. We also discovered that plates have a higher tissue modulus than rods, suggesting different degrees of mineralization. Furthermore, the tissue mineral density correlated strongly but distinctly with tissue modulus in the axial and lateral directions, providing descriptions on how spatially heterogeneous mineralization at the tissue level affects the tissue modulus. After characterization of the anisotropic and heterogeneous modulus of trabecular bone at the tissue level, we then sought to investigate its contribution to apparent-level mechanical properties, including apparent Young’s modulus and yield strength. Non-linear FE voxel models incorporating experimentally determined anisotropy and heterogeneity were created from micro-computed tomography (µCT) images of healthy trabecular bone samples. Apparent Young's modulus and yield strength predicted by the models were compared to and correlated with gold standard mechanical testing measurements, as well as to the same FE models without incorporation of anisotropy and/or heterogeneity. We discovered that the anisotropic model prediction was highly correlated and indistinguishable from mechanical testing measurements. However, the prediction power of the model was not enhanced by incorporating anisotropy and heterogeneity (compared to a homogeneous and isotropic model), suggesting that variances in tissue-level material properties contribute minimally to the apparent level bone behaviors in healthy bone. However, the possibility remained that a more substantial contribution could arise in diseased bone, particularly diseases in which tissue-level properties are compromised. Therefore, we studied trabecular bone in two diseased conditions – subchondral bone in human knees affected by osteoarthritis and pelvic bone affected by adolescent idiopathic sclerosis – to see how disease can alter the tissue-level and, consequently, apparent-level bone mechanics. In OA bone, we found a significant decrease in tissue modulus in the subchondral bone under severely damaged cartilage compared to control, which provides an explanation for a minimal increase in apparent stiffness with an almost doubled bone volume fraction. In AIS bone, no differences were found in tissue-level or apparent level Young’s modulus compared to control. However, the mineral density was found to play a distinct role in the modulus of growing bone tissue compared to mature bone

A Quantitative MRI Protocol for Assessing Matrix and Mineral Densities and Degree of Mineralization of Human Cortical Bone

Two categories of bone disease, osteoporosis and osteomalacia, affect bone in different ways: bone mineral and matrix are lost in roughly equal proportions in osteoporosis, while only mineral is depleted in osteomalacia. The difference between these disorders is in bone mineralization: the mass of mineral per volume of bone matrix, excluding pore spaces. Standard clinical examinations measure x-ray attenuation to infer mineral density. However, bone mineral density alone cannot fully describe bone health. Advances in solid-state 31P and 1H magnetic resonance imaging (MRI) have enabled quantification of the densities of extremely short-lived bone mineral 31P and matrix-bound water 1H signals as surrogates for bone mineral and matrix densities. The ratio of these two measurements provides the degree of mineralization of bone (DMB). In this dissertation, the relaxation properties of bone mineral 31P and water 1H were analyzed, the surrogacy of bound water concentration for bone matrix density was established, and measurements of bone mineral 31P and matrix-associated water 1H densities in human bone specimens were designed and implemented on clinical scanners. Although bone mineral 31P longitudinal relaxation time (T1) increased and effective transverse relaxation time (T2*) decreased with increasing field strength, the predicted signal-to-noise ratio (SNR) increased slightly. Also, the short-T2* fraction of bone water calculated by 1H bi-component fitting was correlated with porosity and matrix density at 1.5 T, but these associations weakened as field strength increased. In contrast, short-transverse relaxation time (T2) fraction was highly correlated with gold-standard measurements, suggesting the superiority of T2-based methods for separation of bound and pore water fractions. Additionally, single adiabatic inversion-recovery zero echo time (SIR-ZTE) 1H density was correlated negatively with porosity and positively with matrix and mineral densities, suggesting that this MRI method provides a surrogate measure of bone matrix density. Finally, both bone mineral 31P and matrix-associated 1H densities in human cortical bone specimens were correlated negatively with porosity and age, and positively with peripheral quantitative computed tomography (pQCT) density. As expected, DMB was uncorrelated with porosity, age, or pQCT density. This work established the feasibility of image-based quantification of bone mineral and bound water densities using clinical hardware